[Bug]: Doesn't work with Claude models via LiteLLM

### Before submitting

- [x] I searched existing issues and did not find a duplicate.
- [x] I included enough detail to reproduce or investigate the problem.

### Area

apps/web

### Steps to reproduce

1. Start the app
2. Start a new thread for an existing project
3. Select "Claude" -> "Claude Opus 4.6"
4. T3 Code requires a login (although via Claude Code CLI, all works without any login requirements)
    - "Not logged in · Please run /login" 

---

Another way (since LiteLLM uses OpenAI-compatible API):
1. Start the app
2. Go to Settings -> Models -> Codex -> Custom model slug -> `claude-opus-4-6`
3.  Start a new thread for an existing project
4. Select "Codex" -> `claude-opus-4-6`
5. Error: `Provider turn start failed - Error: Provider adapter request failed (claudeAgent) for thread.turn.start: Thread '89e787be-e659-46bf-b18b-935b6c49...`

### Expected behavior

All would work like it works in the Claude CLI tool - with no issues and no auth required

### Actual behavior

Requires a login or shows an error

### Impact

Blocks work completely

### Version or commit

0.0.13 (2a237c20019a)

### Environment

macOS 15.7.4 (24G517)

### Logs or stack traces

Our company uses LiteLLM to provide access to different models via the "Google Vertex AI Platform". 
I have an internal tool running on `http://localhost:36253` (this is a local LiteLLM proxy, I assume).
I just have these envs set in my `~/.zshrc`, and Claude Code CLI works without any login requests:

```shell
// Claude Code
export ANTHROPIC_BASE_URL="http://localhost:36253"
export ANTHROPIC_AUTH_TOKEN="REDACTED"
export CLAUDE_CODE_DISABLE_EXPERIMENTAL_BETAS="1"
export DISABLE_TELEMETRY="1"
export DISABLE_ERROR_REPORTING="1"

// Codex CLI
export OPENAI_BASE_URL="http://localhost:36253"
export OPENAI_API_KEY="REDACTED" // same as for `ANTHROPIC_AUTH_TOKEN`
```

Here's additional metadata about available LiteLLM models (from internal tool API call):

```json
{
  "data": [
    {
      "id": "gpt-5-mini",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-2-medium",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-codex-medium",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-opus-4-5-20251101",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-opus-4-6",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gemini-3-flash-preview",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-1-low",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gemini-3-pro-preview",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gemini-embedding-001",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-1-high",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-high",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-codex-low",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-1-codex-high",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-4-low",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-3-5-haiku-20241022",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-1-medium",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-1-codex-low",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gemini-2-5-pro",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-low",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-4-high",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-3-7-sonnet-20250219",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-opus-4-1-20250805",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-1-codex-medium",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-3-codex-low",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-haiku-4-5-20251001",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gemini-3-1-pro-preview",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-opus-4-20250514",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-sonnet-4-5-20250929",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-medium",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-2-high",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-sonnet-4-6",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-3-codex-high",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-4o-mini",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-4-medium",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-2-low",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-3-codex-medium",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gemini-2-5-flash",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "gpt-5-codex-high",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    },
    {
      "id": "claude-sonnet-4-20250514",
      "object": "model",
      "created": 1761865200,
      "owned_by": "openai"
    }
  ],
  "object": "list"
}
```

Here's an example of `opencode.json` config that works just fine as well:

```json
{
  "$schema": "https://opencode.ai/config.json",
  "mcp": {
    "devinfra": {
      "type": "local",
      "command": ["dp-devinfra", "mcp"],
      "enabled": true
    }
  },
  "provider": {
    "litellm-proxy": {
      "npm": "@ai-sdk/openai-compatible",
      "name": "LiteLLM Proxy",
      "options": {
        "baseURL": "http://localhost:36253/v1",
        "apiKey": "cloudflare"
      },
      "models": {
        "claude-opus-4-6": {
          "name": "Claude Opus 4.6 (via LiteLLM)",
          "limit": {
            "context": 200000,
            "output": 32768
          }
        },
        "claude-sonnet-4-6": {
          "name": "Claude Sonnet 4.6 (via LiteLLM)",
          "limit": {
            "context": 200000,
            "output": 64000
          }
        },
        "claude-haiku-4-5-20251001": {
          "name": "Claude Haiku 4.5 (via LiteLLM)",
          "limit": {
            "context": 200000,
            "output": 8192
          }
        },
        "gpt-5-2-high": {
          "name": "GPT-5.2 High (via LiteLLM)",
          "limit": {
            "context": 272000,
            "output": 128000
          }
        },
        "gpt-5-high": {
          "name": "GPT-5 High (via LiteLLM)",
          "limit": {
            "context": 272000,
            "output": 128000
          }
        },
        "gpt-5-mini": {
          "name": "GPT-5 Mini (via LiteLLM)",
          "limit": {
            "context": 272000,
            "output": 128000
          }
        },
        "gemini-3-1-pro-preview": {
          "name": "Gemini 3.1 Pro (via LiteLLM)",
          "limit": {
            "context": 1048576,
            "output": 65535
          }
        },
        "gemini-2-5-flash": {
          "name": "Gemini 2.5 Flash (via LiteLLM)",
          "limit": {
            "context": 1048576,
            "output": 65535
          }
        }
      }
    }
  }
}
```

### Screenshots, recordings, or supporting files

<img width="829" height="769" alt="Image" src="https://github.com/user-attachments/assets/bf83a15d-eb3e-4303-bdb6-ae3fd8247ed9" />

<img width="838" height="774" alt="Image" src="https://github.com/user-attachments/assets/f8a1bb60-0bf5-4ecf-a04e-1f8f3960c014" />

### Workaround

_No response_

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[Bug]: Doesn't work with Claude models via LiteLLM #1225

Before submitting

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[Bug]: Doesn't work with Claude models via LiteLLM #1225

Description

Before submitting

Area

Steps to reproduce

Expected behavior

Actual behavior

Impact

Version or commit

Environment

Logs or stack traces

Screenshots, recordings, or supporting files

Workaround

Metadata

Metadata

Assignees

Labels

Type

Projects

Milestone

Relationships

Development

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